I was trying to simulate the Secretary problem in JS, expecting to get a value of 1/e (~37%), but what I am getting is much less (~10%), and it was changing, increasing people would decrease it.

This is what I tried, I think the error might be the `let x=new Array(people).fill(0).map(e=>Math.random()) `

. I was expecting 37%, but got ~10%

//number of people, and also number of results let people=100 //multiple trials to smooth data let trials=1000; let results=new Array(people).fill(0); // creates a percent, i/people, for each initial group that is "turned down" for (var i=0;i<people;i++) { // runs a few times to smooth data for (var j=0;j<trials;j++) { //x is new random set of people, values in [0,1] let x=new Array(people).fill(0).map(e=>Math.random()); //"rejected set" let min=Math.max(...x.splice(0,i)); //select the first person better than the "rejected" set let select=0; let selected=false for (var k of x) { if (k>=min && !selected) { select=k; selected=true; } } //increase results by selected or last person results[i]+=select!=0?select:x[x.length-1]; } } //strategy to get highest average score console.log("Best strategy: "+(results.indexOf(Math.max(...results))/people*100)+"%");

I also plotted some of the data on desmos here.

## Advertisement

## Answer

I don’t understand how you count the number of successful trials to compute the probability. Try to replace the counting logic as follows.

for (var k of x) { if (k > min && !selected) { select = k; selected = true; } else if (k > select && selected) { selected = false; break; } } //increase results by selected or last person results[i]+= selected

Basically, your trial is successful only when the first higher than `min`

value is the total maximum. This gives values close to `1/e*100`

for me.